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So now we need to evaluate our model as we have, of course, now the model if we want to well, see

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how the model is just this is a kind of we already wrote it here.

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So model.

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Evaluation.

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We can see the model we have is a sequential model.

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Of course, like two input and one output feature.

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And this is the all of the well, the sizes of the model.

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So.

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The network we have is supposed to work like this.

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We give it X and we give it time and it will give us u.

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So let's do it first.

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We make another computational domain and this time we make it smaller like H equals 0.01.

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In the past it was 0.1, I think.

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Yeah.

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0.1.

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So we don't really care.

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Or the of course our our.

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Why is that?

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Yeah.

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Our training model is is only trained on a very specific boundary and initial condition.

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And this is a problem.

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But in general, if you want a model that works in a wide range of boundary conditions and initial conditions,

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you have to train it on much more boundary conditions and initial conditions.

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However, let's change a little bit to just to make it more exciting, just to change it, the computational

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domain.

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But of course, in your case you have to consider the initial condition, boundary condition to get

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a very quick results from this model in the training part of it.

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So here or like a good result like now it will we will only change one thing which is the the grid.

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But in Pence, the general dream or like motivation of Pence is we need a model that is capable to give

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us approximation on a wide range of.

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Initial conditions and boundary conditions.

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So this is actually why we do it.

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But other than, you know, the fun of it.

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Arrange is we just keep it the same boundary condition to make it work well.

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You can of course change the boundary condition and see how your model behaves.

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T is from 0 to 1.

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For me, it just.

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I will just put it as is.

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And yeah, this is the the.

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I'm like, I'm not going to train it on different boundary conditions and initial conditions and so

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on.

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But it it if you to get a good answers, we always have to consider this kind of thing.

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So here torch dot um stack.

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And torch dot mesh the same thing.

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Grid X and T.

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And reshape.

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Two minus one.

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Transpose it.

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And x equals x.

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To.

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Net dot x dot.

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Device.

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Device.

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Device.

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And of course the X will be this way.

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It's already put on cuda.

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And if you want to see the shape.

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It's 2000 by two, 2000 points by, of course, X, just two, 2000 different rows, and then two is

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X and T.

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So so basically now what we need is to predict it.

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And.

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A model.

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Is equals to net dot.

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Model.

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And.

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Model.

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Noel.

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Evaluation.

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And with.

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Torch?

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No.

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Grad.

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Why predict?

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Predict equals model.

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X dot reshape.

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If or just we can put it like this.

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Why?

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The dict equals.

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Dot reshape.

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The shape length of X.

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And length of T.

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So we will get a kind of beautiful.

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A matrix that we can plot numpy.

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Shift into.

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And then why predict we can see the shape of it?

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And then we can see the actual values of this.

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And let's now of course, contour plot it so it's in s dot set.

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This style.

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No white.

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P l t dot.

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Bigger.

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Big.

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Size equals.

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Five and three.

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DPI.

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And just the.

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The solution is in s dot heat.

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Map.

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Y predict.

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C map equals jet.

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Oh, sorry.

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Git shift.

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Enter.

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And we look at the drawing.

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So basically we start by having a sine wave and it will converge to something that looks like a step

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and actually we can look at it.

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PLT dot.

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We will print this part and this part so the left side and the right side.

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And of course, you can in between like plot.

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Why?

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Predict.

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All of it and zero shift enter.

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So start will be a wave, which is this swipe predict we're printing all the values at time equals zero.

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We can see it looks like this.

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And at the end of it, just let's take it.

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Uh, like, minus one.

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We can see the step function if you want in between like you have to put like I think this is 20,000.

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Uh, the shape is 100 steps.

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So like, we can consider like 50.

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It gives us something in between.

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We see.

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At ten.

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It's still it's it didn't converge into this step.

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A 40.

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It's more.

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100.

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We cannot.

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99.

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We can.

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So this is the last one and maybe just put it 40.

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But for a little bit too already kind of converged.

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30.

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Yeah, it's a little bit.

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We can see the kind of wavy shape still and here is more sharp.

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So this is how to solve burgers equation using PyTorch.